Why is my road offset from it's parent bezier (wrapped to a sphere)?
Do you really need one unique road?

If that's the case, you could create a sphere, a curve, and use the Snap option to stick the curve to the surface of the sphere, then gradually scale down the sphere so that the curve also scales down.

If you don't absolutely need one unique road (which in my opinion is the case in this picture) you could fake this kind of object this way:


Create your road segment, apply the scale and the rotation, give it an image texture.





Create a curve. Give your road segment an Array modifier, Fit Type > Fit Curve, and a Curve modifier.





Duplicate your curve + object, rotate and move it as you like, scale the curve (and only the curve).